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IrinaK [193]
3 years ago
6

Represent 31/42 as a decimal. Round to 2 decimal places.

Mathematics
1 answer:
torisob [31]3 years ago
7 0

Answer: 0. 74

Step-by-step explanation: 31/42= 0.738095238095= 0.74

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Marie has a rectangular board 12 inches by 16 inches around which she wants to put a uniform border of sherlls. if she has enoug
Ede4ka [16]
Area of rectangular board = length (inches) x width (inches) = 12" x 16" = 192 in²

Area of the border is given as 128 in²

Adding the area of the board and the border gives (192 + 128)in² = 320 in²

Set this up as the algebraic equation (x + 12)(x + 16) = 320 and solve for x:

Remember to use the FOIL method, which is multiplying the terms in the order of first, outer, inner, last.

x² + 12x + 16x + 192 = 320

x² + 28x + 192 - 320 = 0

x² + 28x - 128 = 0

solve for the two x values:

(x + 32)(x - 4) = 0, and knowing we only need the positive x value

x = 4 or 4 inches is the width of the border



5 0
4 years ago
If line uw bisects angle tuv,, m angle tue = (13x-5) and angle wuv = (7x+31) find the value of x
scZoUnD [109]

The value of x will be 6

<u><em>Explanation</em></u>

According to the below diagram, UW is the angle bisector of ∠TUV

<u>That means,</u>  \angle TUW = \angle WUV

Given that,  \angle TUW = 13x-5 and \angle WUV= 7x+31

So, the equation will be......

13x-5=7x+31\\ \\ 13x-7x=31+5\\ \\ 6x=36\\ \\ x=\frac{36}{6}=6

So, the value of x will be 6.

4 0
4 years ago
Starting at the park, Jake bikes 3 blocks north, 4 blocks east, 4 blocks south, 7 blocks west, and 1 block north. How many block
yan [13]
I'll use a coordinate plane for this since it's easier (for me) :)

Red = park
Blue = his trail
Pink = distance from park = 3

Hope this helped! Please comment or DM me if you have anymore questions or don't understand :)

7 0
3 years ago
3. If the scale factor in a dilation is a number between 0 and
REY [17]

Answer: Reduction

Step-by-step explanation: If the scale factor of a dilation is between 0 and 1, the image will be smaller than the object, a reduction. It would only be an enlargement if the scale factor is greater than 1.

4 0
3 years ago
A geometric sequence is defined by the general term tn = 75(5n), where n ∈N and n ≥ 1. What is the recursive formula of the sequ
andreyandreev [35.5K]
The correct answer is C) t₁ = 375, t_n=5t_{n-1}.

From the general form,
t_n=75(5)^n, we must work backward to find t₁.

The general form is derived from the explicit form, which is
t_n=t_1(r)^{n-1}.  We can see that r = 5; 5 has the exponent, so that is what is multiplied by every time. This gives us

t_n=t_1(5)^{n-1}

Using the products of exponents, we can "split up" the exponent:
t_n=t_1(5)^n(5)^{-1}

We know that 5⁻¹ = 1/5, so this gives us
t_n=t_1(\frac{1}{5})(5)^n&#10;\\&#10;\\=\frac{t_1}{5}(5)^n

Comparing this to our general form, we see that
\frac{t_1}{5}=75

Multiplying by 5 on both sides, we get that
t₁ = 75*5 = 375

The recursive formula for a geometric sequence is given by
t_n=t_{n-1}(r), while we must state what t₁ is; this gives us

t_1=375; t_n=t_{n-1}(5)

3 0
4 years ago
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